THE APPLICATION OF ALGEBRA 
308 
PROBLEM XXXVIII. 
Let A and B be two equal weights, made fast to the 
ends of a thread, or perfectly flexible line pFnQq, sup 
ported by two pins, or tacks, P, Q, in the same horizontal 
plane; over which pins the line can freely slide either icay; 
and let C be another weight, fastened to the thread, in 
the middle, between P and Q : now the question is, to find 
the position of the weight C, or its distance below the 
horizontal line PQ, to retain the other two weights A and 
B in equilibrio. 
Let PR { := |*PQ) be denoted by a, and R« (the 
distance sought) by x ; and then Pn, or Qn, will be re- 
forccs, it will be, as \/ a 1, + x x (P;*) : x (Rh) :: the 
whole force of the weight A in the direction P«, to 
its force in the direction nR, whereby it en- 
V a x 4- x 7 
deavours to raise the weight C ; which quantity also 
expresses the force of the weight B in the same direc 
tion : but the sum of these two forces, since the weights 
are supposed to rest in equilibrio, must be equal to that 
of the weight C; that is, —j- 2 —.—= C ; whence we 
\/a x + x 2 
have 4A*x 1 rz C i a x f C 2 x*, and consequently x zx 
aC